A note on the sum of distances under a diameter constraint

We give an upper bound for the value 1/n(2) Sigma (n)(i,j=1) parallel tox(i ) - x(j)parallel to (2), where x(1), ..., x(n) are points in the Euclidean plane R-2 with parallel tox(i) - x(j)parallel to (2) less than or equal to 1 for all 1 less than or equal to i, j less than or equal to n and where pa rallel to.parallel to (2) denotes the Euclidean norm. Moreover we give an u pper bound for the number k(2) = sup r(X, parallel to.parallel to (2)), whe re X is a compact connected subset of R-2 with diameter one and where r(X, parallel to.parallel to (2)) denotes the rendezvous number of (X. parallel to.parallel to (2)).